The present invention relates generally to magnetic resonance—(MR) imaging and, more particularly, to a method and apparatus of correcting distortion in an MR image caused by an implant.
When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B1) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, or “longitudinal magnetization”, MZ, may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment Mt. A signal is emitted by the excited spins after the excitation signal B1 is terminated and this signal may be received and processed to fill a data acquisition or k-space matrix. The data stored in the k-space matrix may then be processed to form an image.
When utilizing these signals to produce images, magnetic field gradients (Gx, Gy, and Gz) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received NMR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques.
It is well known that, in the presence of a foreign object, the magnetic fields used in MR imaging often induce magnetic fields about the foreign object that can cause noticeable distortion in the resulting MR image. All materials have some form of magnetism, which is measured by its respective magnetic susceptibility, χ. Magnetic susceptibility is a measure on how a material reacts to external magnetic fields. This “reaction” of materials to magnetic fields is fundamentally manifested in the magnetic field they induce in response to the external field. Higher magnitudes of magnetic susceptibility induce more severe magnetic fields. In magnetic resonance, a very large magnetic field of relative spatial homogeneity is used to polarize nuclear (or electronic) spins. When a material is placed in this magnetic field, its magnetic susceptibility distribution causes an induced magnetic field. It is this induced magnetic field that can cause distortion in MR images. On its own, the human body induces such fields. However, the magnetic susceptibilities of organic tissue and air have magnitudes roughly 10-100 times less than the relative magnetic susceptibilities of metallic implant components and their surrounding tissue, depending on the type and shape of the metal used in the implant. Therefore, the magnetic fields induced by metallic implants are far more severe and troublesome than the induced fields typically dealt with in biological magnetic resonance applications.
Techniques have been developed to correct distortion caused by a substance's induced magnetic field. One such technique is the “line-integral” technique. The basic principle of this technique is described hereinafter and assumes distortion in a single dimension.
First, two images [I1(x1) and I2(x2)] are acquired with equal and opposing imaging gradients in the desired direction of desired distortion correction (i.e. the phase-encode direction in EPI images or the readout direction of spin-echo images near metal implants). The image distortion then occurs in opposite directions, but with different character due to the added superposition of imaging gradient fields with opposite sign. For each line in the distorted direction, a boundary is found at one of the images and then the distance between this boundary and the corresponding point in the other image is estimated by integrating each image in the distorted direction. Where the integrals match, is where the two points correspond to one another. The midpoint of the two points is then the point where signal would lie in a non-distorted image [I0(x)]. This process is repeated until a full mapping of points in each image is uncovered:x→x1 and x→x2  [1]This is effectively the same as knowing the magnetic field map at each point in the image, since:x1=x+αB0(x), and x2=x−αB0(x);  [2]where α is a known constant, and:x=(x1+x2)/2  [3]
Equation [3] is the mathematical basis of the line-integral method previously described. Knowing this mapping, the intensity of the non-distorted image is also uncovered as:I(x)=2 I1(x1)I2(x2)/[I1(x1)+I2(x2)].  [4]
On its own, the line-integral method has not been successfully demonstrated or utilized near metallic implants in spin-echo images. There is a clear reason for this lack of application. Equations [2-4] are valid under the assumption that the mappings generally expressed in Equation [1] are monotonic (i.e. the distorted images map back to one and only one point in the non-distorted image). This mathematical condition is violated where the extraneous magnetic field inhomogeneity gradient is greater than the gradient used to encode the MR images in the distorted direction. In regions where this mathematical condition is violated, both the mappings and the intensity calculation [4] become invalid. That is, the mappings and intensity calculation become invalid for correcting distortions in the slice direction if the magnetic field inhomogeneity gradient is greater than the slice-select gradient. This violation also occurs in the readout direction when the magnetic field inhomogeneity gradient in the readout direction is greater than the readout gradient. Unfortunately, these very inequalities are quite often encountered near metallic implants. Therefore, the typical line-integral based repair of distorted images cannot be used in such regions. Furthermore, it is generally believed not possible for the typical line-integral method to perform any “self-diagnosis” in identifying regions where its methods are limited. This quandary renders the standard application of the line-integral method virtually useless near metallic implants. Extra information would be needed to tell the line-integral method where to evaluate Equations [2-4] and where other methods should be implemented. An operator could determine regions by guessing where the mathematical condition is not violated and then apply the method in those regions. However, as one skilled in the art will readily acknowledge, this guessing game would be unsuccessful in accurately defining the boundaries of the regions.
One skilled in the art would immediately appreciate the benefit of accurately determining regions where the inequality is valid and not valid in spin-echo images. If the regions are defined accurately, more robust MR images of areas where implants are present can be created. For example, in the field of arthroplasty, implants are often used for joint repair. Most often, there is a strong need for accurate MR images of the implant and areas in the immediate vicinity of the implant. Without accurately determined regions, accurate conventional MR images are currently unattainable.
It would, therefore, be desirable to have a method of determining a region where the line-integral method can be successfully implemented and determining another region where other methods can be successfully applied to repair distorted MR images.